About the solution
A small box with some volume controls and a microphone amplifies the ambient sound and plays it to the patient. The headphone set up could be anything, though a vibratory conductive speaker like Jawbone makes the most sense to me. To improve on similar technology, there could be a small control box that plugs in and administers a short hearing test. The box takes this into account in how much the relative amplification if provides for each frequency range.
There are many patients who are hard of hearing in the hospital, speech amplicofation should be a right just like a language interpreter. Patients need to understand their medical plans, their discharge instructions, and even their surroundings. I think this could reduce delirium in the hospital as well.